The wee hours (of the night/morning) American British noun phrase
Used to indicate the early hours after midnight, particularly from 1 am to 4 am morning.
Lisa stayed up until the wee hours to handle the immense workload.
I was rehearsing the presentation until the wee hours, that is the reason why I feel sleepy now.
My brother is a night owl, he often surfs Facebook until the wee hours of the morning.
According to the Oxford Dictionary, "wee" has been used since the 1600s in Southern England.